Murray racked-up his 50th Wimbledon match win while Federer reached the quarter-finals for the 14th time as the top two remaining seeds edged closer to a dream title match.
Second seeded Murray, the 2013 champion, eased to a 7-5, 6-1, 6-4 win over fiery Australian Nick Kyrgios and will next face French 12th seed Jo-Wilfried Tsonga.
Federer went equal with Jimmy Connors’ mark of 14 quarter-finals at Wimbledon and tied Martina Navratilova’s all-time Slam record of 306 match wins by seeing off Steve Johnson of the United States 6-2, 6-3, 7-5.
Kyrgios, the 15th seed who defeated Rafael Nadal at the tournament in 2014, did not force a break point on Murray’s serve as he slipped to his fifth loss in five meetings against the world number two.
“The first set was very tight. I managed to get the break at 6-5 but it was very tight up to that point,” explained Murray.
Kyrgios condemned his own performance.
“The first set was OK but after that it was pathetic,” said the 21-year-old.
Seven-time champion Federer, the third seed, next takes on Croatia’s Marin Cilic for a place in the semi-finals.
Cilic, the ninth seeded Croat, progressed to his third successive Wimbledon quarter-final when Japanese fifth seed Kei Nishikori pulled out of their last-16 clash with a rib injury in the second set.
Federer has a 5-1 record over Cilic but the big-server stunned the 17-time major champion in the US Open semi-finals in 2014 on his way to his maiden Grand Slam title.
“He blew me off the court and I hope to get him back,” said 34-year-old Federer.
Sam Querrey followed up his shock defeat of defending champion Novak Djokovic by beating French veteran Nicolas Mahut 6-4, 7-6 (7/5), 6-4 to reach his first Grand Slam quarter-final.
Querrey, the 28th seed, is the first American in the last-eight at Wimbledon since Mardy Fish in 2011.
Querrey will next face Canadian sixth seed Milos Raonic, who came back from two sets down for the first time in his career to beat Belgium’s David Goffin.
Raonic, a Wimbledon semi-finalist in 2014, won 4-6, 3-6, 6-4, 6-4, 6-4.
In an all-Czech match-up, world number 64 Jiri Vesely and 10th seeded 2010 runner-up Tomas Berdych were tied at two sets each when play was halted for the night.
Vesely had saved five match points.
Williams sisters on track
The winner faces French 32nd seed Lucas Pouille, who made the last eight of a Slam for the first time by seeing off Bernard Tomic, 6-4, 4-6, 3-6, 6-4, 10-8.
Cibulkova could be forced to postpone her wedding after knocking out world number three Agnieszka Radwanska.
Cibulkova is due to marry fiance Miso Navara in her hometown of Bratislava on Saturday.
But the confetti and wedding cake might be put on hold because the Slovakian 19th seed has advanced to the quarter-finals with a 6-3, 5-7, 9-7 victory against Radwanska.
Cibulkova’s walk down the aisle will have to wait if she defeats Russian world number 50 Elena Vesnina in Tuesday’s quarter-finals.
“If I win, then we will change it. We will postpone it because it will be a lot of rush,” Cibulkova said.
Vesnina won 5-7, 6-1, 9-7 against compatriot Ekaterina Makarova, who is her long-term doubles partner.
Serena Williams powered into her 12th Wimbledon quarter-final as the defending champion clinched a 7-5, 6-0 victory over Russian 13th seed Svetlana Kuznetsova.
World number one Williams hit 43 winners and served 14 aces as she won the last nine games on Centre Court to remain on course for a record-equalling 22nd major title and a seventh Wimbledon crown.
“She has played really well against me in the past and she beat me earlier this year so I know that I had to play really well to win this,” Williams said of the Kuznetsova clash.
The 34-year-old, an eight-time Wimbledon finalist, will next play Russian 21st seed Anastasia Pavlyuchenkova, a 6-3, 6-3 winner over Coco Vandeweghe of the United States.
Venus Williams became the oldest Wimbledon women’s quarter-finalist for 22 years as the five-time champion defeated Spanish 12th seed Carla Suarez Navarro 7-6 (7/3), 6-4.
Venus now faces Kazakhstan’s Yaroslava Shvedova, a 6-2, 6-4 winner over Czech 28th seed Lucie Safarova.
German fourth seed and Australian Open champion Angelique Kerber cruised into her third Wimbledon quarter-final with a 6-3, 6-1 thrashing of Japanese world number 49 Misaki Doi.
Kerber plays Romania’s Simona Halep, who fought back to reach her second Wimbledon quarter-final with a 6-7 (5/7), 6-4, 6-3 win against American ninth seed Madison Keys.